I've been trying to figure out a way to make a snow free area in my run too. I've given up on tarps because no matter how tightly they are tied down or how steeply I've made the slope or support under it (tall A frame or curved hog panel), the wind picks it up and shreds it. If it survives the winds of fall, the snow makes it sag. I've been thinking of making a metal roof "porch" to have a permenent solution. I know I'd have to have it angled fairly steep to help the snow slide off. Sounds like I will have to make sure there is plenty of support to not have sagging issues with metal.
CG
How steep the metal needs to be, depends on how much support it has. A strong support system can hold a crazy amount of weight...
I built my duck coop with rotted wood, so made the metal roof have a steep slope.
Raking the roof twice in the middle of the night whenever it snows.....is not a fun winter activity. Set it up so you do not have to rake or shovel.